a,b,c為正實數,
且a+b+c=1,
則√a+√b+√c的最大值是多少？
解釋&過程,please~
問數,求最大值,求最大值,求最大值,求最大值
2008-05-15 6:29 am
回答 (2)
2008-05-15 7:00 am
✔ 最佳答案
AM < or = QM[sqrt(a) + sqrt(b) + sqrt(c)]/3 < or = sqrt{([sqrt(a)]^2 + [sqrt(b)]^2 + [sqrt(c)]^2)/3}
[sqrt(a) + sqrt(b) + sqrt(c)]/3 < or = sqrt[(a+b+c)/3] = sqrt(3/3) = 1
so sqrt(a) + sqrt(b) + sqrt(c) < or = 3
i.e. max value of sqrt(a) + sqrt(b) + sqrt(c) is 3
2008-05-15 11:56 pm
AM ≤ QM
(√a + √b + √c) / 3 ≤ √[(√a^2 + √b^2 + √c^2) / 3]
(√a + √b + √c) ≤ √[3 (a + b + c)]
(√a + √b + √c) ≤ √3
(√a + √b + √c) / 3 ≤ √[(√a^2 + √b^2 + √c^2) / 3]
(√a + √b + √c) ≤ √[3 (a + b + c)]
(√a + √b + √c) ≤ √3
收錄日期: 2021-04-20 19:28:46
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080514000051KK02948